Sørensen began karting in 1994 and entered formula racing in 2006 with Formula Ford Denmark. After a partial ADAC Formel Masters season in 2008, he joined Renault's driver development programme in 2009 alongside Davide Valsecchi and Charles Pic, competing in Formula Renault 2.0. When that programme was closed due to financial difficulties later that year, his career was set back significantly.
Recovering in mid-2010 with a drive in the German Formula Three series for Brandl Motorsport, Sørensen went on to finish runner-up in 2011 after a close battle with eventual champion Richie Stanaway. He also took a one-off Formula 3 Euro Series entry at Silverstone in 2011 with Mücke Motorsport, winning the reverse-grid race.
Lotus offered him a Formula Renault 3.5 test in 2012, and he impressed enough to secure a race seat alongside former rival Stanaway. He took his first series win at Spa and finished the season in joint fifth. The 2013 campaign brought further podiums and victories — including pole and wins in both Red Bull Ring races — despite ongoing reliability issues.
In 2014 Sørensen moved to the GP2 Series with MP Motorsport from Silverstone onwards, scoring his first GP2 win at Sochi. He completed a full 2015 GP2 season with Carlin after Felipe Nasr departed for Formula One. During the 2013–14 period he was also a Lotus F1 team test driver, undertaking a tyre test at Circuit Paul Ricard.
Sørensen joined Aston Martin Racing for the 2015 FIA World Endurance Championship alongside Nicki Thiim, becoming a full-time factory driver. The partnership between Sørensen and Thiim — known informally as the "Dane Train" for the duo's Danish nationality — became one of the most consistent pairings in GTE racing. Their first endurance win together came in Austin in 2016, and that year they won the LMGTE Pro class championship with Aston Martin's No. 95 Vantage GTE.
A second LMGTE Pro championship followed in the 2019–20 extended season. Sørensen returned to the WEC in 2022 for a full season with TF Sport, piloting the No. 33 Aston Martin Vantage AMR alongside Ben Keating and Florian Latorre in the LMGTE Am class; the trio won the class title. Though Sørensen was absent from the WEC grid in 2023, he was present at Le Mans that year as part of GMB Motorsport's GTE Am entry alongside Jens Reno Møller and Gustav Birch. His younger brother, Lasse Sørensen, has also pursued a professional racing career.
Three WEC class titles with a single manufacturer — Aston Martin — in GT racing across six seasons of competition represents a level of consistency unusual even in endurance racing. Sørensen's career arc, from a junior programme shutdown that might have ended a lesser driver's prospects to becoming one of the faces of Aston Martin's factory racing efforts, reflects both resilience and a natural affinity for long-distance racing. His work alongside Thiim helped establish Aston Martin as a front-running force in GTE Pro during the mid-to-late 2010s.